A Parallel Abductive Query Answering in Probabilistic Logic Programs GERARDO I. SIMARI, University of Oxford JOHN P. DICKERSON, Carnegie Mellon University AMY SLIVA, Northeastern University V.S. SUBRAHMANIAN, University of Maryland College Park Action-probabilistic logic programs (ap-programs) are a class of probabilistic logic programs that have been extensively used during the last few years for modeling behaviors of entities. Rules in ap-programs have the form “If the environment in which entity E operates satisfies certain conditions, then the probability that E will take some action A is between L and U ”. Given an ap-program, we are interested in trying to change the environment, subject to some constraints, so that the probability that entity E takes some action (or combination of actions) is maximized. This is called the Basic Abductive Query Answering Problem (BAQA). We first formally define and study the complexity of BAQA, and then go on to provide an exact (exponential time) algorithm to solve it, followed by more efficient algorithms for specific subclasses of the problem. We also develop appropriate heuristics to solve BAQA efficiently. The second problem, called the Cost-based Query Answering (CBQA) problem checks to see if there is some way of achieving a desired action (or set of actions) with a probability exceeding a threshold, given certain costs. We first formally define and study an exact (intractable) approach to CBQA, and then go on to propose a more efficient algorithm for a specific subclass of ap-programs that builds on the results for the basic version of this problem. We also develop the first algorithms for parallel evaluation of CBQA. We conclude with an extensive report on experimental evaluations performed over prototype implementations of the algorithms developed for both BAQA and CBQA, showing that our parallel algorithms work well in practice. Categories and Subject Descriptors: I.2.3 [Deduction and Theorem Proving]: Probabilistic Reasoning; I.2.8 [Knowledge Representation Formalisms and Methods]: Heuristic Methods General Terms: Algorithms, Languages Additional Key Words and Phrases: Probabilistic Reasoning, Imprecise Probabilities 1. INTRODUCTION Action probabilistic logic programs (ap-programs for short) [Khuller et al. 2007] are a class of the extensively studied family of probabilistic logic programs (PLPs) [Ng and Subrahmanian 1992; 1993; Kern-Isberner and Lukasiewicz 2004]. ap-programs have been used extensively to model and reason about the behavior of groups and an application for reasoning about terror groups based on ap-programs has users from over 12 US government entities [Giles 2008]. ap-programs use a two sorted logic where there are “state” predicate symbols and “action” predicate symbols 1 and can be 1 Action atoms only represent the fact that an action is taken, and not the action itself; they are therefore quite different from actions in domains such as AI planning or reasoning about actions, in which effects, preconditions, and postconditions are Author addresses. Gerardo I. Simari: Department of Computer Science, Wolfson Building, Parks Road, University of Oxford, Oxford OX1 3QD, UK. John P. Dickerson: 9219 Gates-Hillmman Center, Carnegie Mellon University, Pittsburgh, PA 15213, USA. Amy Sliva: College of Computer and Information Science, 256 West Village H, Northeastern University, Boston, MA 02115, USA. V.S. Subrahmanian: Department of Computer Science, University of Maryland College Park, College Park, MD 20742, USA. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701 USA, fax +1 (212) 869-0481, or permissions@acm.org. c  2012 ACM 1529-3785/2012/04-ARTA $10.00 DOI 10.1145/0000000.0000000 http://doi.acm.org/10.1145/0000000.0000000 ACM Transactions on Computational Logic, Vol. V, No. N, Article A, Publication date: April 2012.